Velocity time graphs

Goals for today

• Discuss V-T graphs

• Homework– In the books p 338-339 proms 2-7, 10-11,

14-16, 22-28-- Graph handout

Test for honors is WednesdayCP is Thursday

Differences between V-t graphs and P-T graphs

• The vertical #’s tell how fast, not location

• V-t does not indicate start position

• Direction is indicated by position on graph, not slope

• Acceleration is indicated differently on each type of graph

Horizontal lines on a V-T graph

Velocity (m/s)

Time (s)

Can you mimic the graph

Using the motion detector

Tilted lines on V-T graphs

V (m/s)

T (m/s)

What do tilted lines mean on a V-T graph?

• The object is changing its velocity

• Acceleration

• How it accelerates is determined by– Location of graph (Above, Below x-axis)– Type of tilt

Acceleration is…

• A change in the velocity of the object

• Tilted lines on a V-T graph indicate acceleration

• Acceleration can be calculated by finding the slope value of these lines

Tilted lines on V-T graphs

V (m/s)

T (m/s)

What kind of motion is indicated on this graph?

V (m/s)

T (s)

What would curves mean on a V-T graph

• Curves would indicate non-constant acceleration

• Think roller coaster rides, when you get pushed against the harness or back into the seat

• The ‘Jerk’

Identify motion for each part of the V-T graph

V (m/s)

T (m/s)

Identify motion for each part of the V-T graph

V (m/s)

T (m/s)

Create a V-t graph that…

• Section 1: Shows constant motion of (-3) m/s for 5 seconds.

• Section 2: Shows constant acceleration (slowing down in the negative direction)

• Section 3: Shows no movement for 5 seconds

• Section 4: Shows constant acceleration (speeding up in the positive direction)

Answer

Homework

• For all graphs:– Find the direction– Constant Velocity or Non-Constant Velocity– Fast, Average or Slow– Faster, Slower (Change in Velocity)

Finding overall displacement from V-T graph

• How far does an object travel if it goes

3 m/s for 10 seconds?

V

t

3

10

Acceleration

• Anytime the velocity of an object changes, the object accelerates

– Getting Faster– Getting Slower– If the motion of object changes direction going

the same speed

Velocity changes if…

Speeding up Slowing down

Velocity changes if…

• The direction of the motion changes, but the speed does not

• This type of acceleration is call centripetal acceleration

Equation for average acceleration

a = (vf - vi) / t

vf = final velocity

vi = initial velocity

t = elapsed time

a = acceleration

Ex #1

• A flowerpot falls off a second story windowsill. The flowerpot start from rest and hits the sidewalk 1.5 s later with a velocity of 14.7m/s. Find the average acceleration.

What information is given?Identify the information.

• 1.5s • Is the time• 14.7 m/s• is the final velocity• Starts from rest• Means that the initial velocity is zero (0)

• “at rest” always means that vi = o

Answer #1

• a = (14.7 – 0) / 1.5 = 9.8

• What are the units?

• (14.7 m/s – 0 m/s) 1.5 s = (m/s) / s

• m / s2

Ex #2

• While driving at an average velocity of 15.6 m/s down the road, a driver slams on brakes to avoid hitting a squirrel. The car stops completely in 4.2 seconds. What is the acceleration of the car?

• Givens15.6 m/s = vi

4.2 s = t

0 = vf

• What you want to solve foracceleration

Solution

a = (0 – 15.6) / 4.2 = (-3.7) m/s2

Questions on homework in book

• Pg 324

• Pg 328

Mr. Baker’s Monster problem

• On a dark and scary night, Mr. Baker was walking down the street at 5.234 m/s. He heard a horrible sound of hundreds of shuffling feet behind him and increased his speed to a new 78.985 m/s. What was the amount of time (in minutes) needed to increase his speed, if his rate of acceleration was 1.9 m/s2 ?

Answer

Given: vi = 5.234 m/s a = 1.9 m/s2

vf = 78.985 m/s

Want: time (in minutes)

a = (vf – vi) / t

1.9 = (78.985 -5.234) / t